Reduced complexity coding system using iterative decoding

ABSTRACT

A concatenated coding scheme, using an outer coder, interleaver, and the inner coder inherent in an FQPSK signal to form a coded FQPSK signal. The inner coder is modified to enable interative decoding of the outer code.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. Provisional Application No.60/285,903, filed Apr. 23, 2001.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under grant no.NAS7-1407. The government may have certain rights in this invention.

SUMMARY

Properties of a channel affect the amount of data that can be handled bythe channel. The so-called “Shannon limit” defines the theoretical limitof amount of data that a channel can carry.

Different techniques have been used to increase the data rate that canbe handled by a channel. “Near Shannon Limit Error-Correcting Coding andDecoding: Turbo Codes,” by Berrou et al. ICC, pp 1064-1070, (1993),described a new “turbo code” technique that has revolutionized the fieldof error correcting codes.

Turbo codes have sufficient randomness to allow reliable communicationover the channel at a high data rate near capacity. However, they stillretain sufficient structure to allow practical encoding and decodingalgorithms.

Feher's patented QPSK, or FQPSK, as described in detail in U.S. Pat.Nos. 4,567,602; 4,339,724; 4,644,565; 5,784,402; and 5,491,457 is acoded modulation scheme. The generic form of FQPSK is based oncrosscorrelated phase-shift-keying. FQPSK maintains a nearly constantenvelope, that is the maximum fluctuation in the envelope is around 0.18dB. This is done by manipulating the pulse shapes of the in-phase “I”and quadrature “IQ” signals using crosscorrelation mapping.

Many different variants of FQPSK are known, including FQPSK-B, which isa bandwidth limited form of FQPSK.

The price of this spectral efficiency of these coded modulation schemesmay be a degradation in the bit error rate performance.

SUMMARY OF THE INVENTION

The present application teaches a new technique which allows additionalpower efficiency and bandwidth efficiency with a simple receiverarchitecture. This technique may use turbo coding techniques, along witha specially configured FQPSK encoder and/or decoder, to form aconcatenated coded modulation scheme.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects will now be described in detail with referenceto the accompanying drawings, wherein:

FIG. 1 shows a conceptual diagram of FQPSK;

FIG. 2 shows an alternative implementation of the baseband signals usingmapping;

FIG. 3 shows full symbol waveforms of FQPSK;

FIG. 4 shows a trellis decoding interpretation used for a receiver;

FIG. 5 shows a bit error rate comparison of the different techniques;

FIG. 6 shows averaged waveforms for the simplified receiver;

FIG. 7 shows at trellis diagram for the simplified receiver;

FIG. 8 shows a simplified implementation of the baseband signals;

FIG. 9 shows a simplified receiver;

FIGS. 10 a-b show original and remapped encoders and trellises for thereceiver to be used in concatenated schemes;

FIGS. 11-13 show embodiments of the improved transmitter and receiver;and

FIG. 14 shows a soft input soft output outer decoder for a rate ½repetition outer code.

DETAILED DESCRIPTION

FQPSK in its standard form is similar to many phase-shift-keyingtechniques which had been previously used. A conceptual diagram of FQPSKis shown in FIG. 1. One advantage of the specific FQPSK system is a 3 dbenvelope reduction based on intentional but controlled crosscorrelationbetween the I and Q channels. This was described by half symbol mappingsof the 16 possible combinations of I and Q channel waveforms that werepresent in the signal, into a specified set of 16 waveform combinations.These 16 waveform combinations were selected in a way that rendered thecrosscorrelated output time continuous. The waveform combinations alsohad unit, normalized, envelopes at each of the I and Q uniform samplinginstants.

Since the crosscorrelation mapping was based on half symbolcharacterization of the signal, there was no guarantee that the slope ofthe crosscorrelated output waveform would be continuous at thetransitions between the half symbol points. In fact, a slopediscontinuity may occur statistically one-quarter of the time.

In a copending patent application, it is suggested to structure thecrosscorrelation mapping into a full symbol by symbol mapping, ratherthan a half symbol by half symbol representation. In fact, thistechnique also has the advantage of enabling data transitions on the Iand Q channels to be described directly. Moreover, this enables areceiver for FQPSK which exploits the specific correlation (memory) thatis introduced into the modulation scheme.

FIG. 2 illustrates the interpretation of FQPSK as a trellis-codedmodulation. The input streams of data bits are split into time-aligned Iand Q symbol streams at half the usual bit rate, so 1/T_(s)=½T_(b). Eachof these symbol streams is passed through specific rate ⅓ encoders. Therate ⅓ encoder 200 for the I stream 200 is different than the rate ⅓encoder 240 for the Q stream 250. The output bits of these encoders arethen considered to be grouped into one of three different categories.

The three categories include a first category of bits that onlyinfluence the choice of the signal in the same channel. A secondcategory of bits only influence the choice of the signal in the otherchannel. A third category of bits influence choices of signals in bothchannels, that is represent crosscorrelation mapping.

Out of the bit sequences from the I encoder 200, the value I3 signal 201is used to determine the signal that is transmitted on the I channel.The value Q0 signal 202, is used to determine the signal transmitted onthe Q channel. The value I2, which is the same as Q1, signal 203, isused to determine both the signals transmitted on I and Q channels.

If d_(ln) and d_(Qn) respectively denote the +1 and −1 I and Q datasymbols in the nth transmission interval and D_(In) ^(Δ) (1−d_(ln))/2and D_(Qn) ^(Δ) (1−d_(Qn))/2 their (0,1) equivalents, then the mappingsappropriate to the I and Q encoders of FIG. 2 areI ₀ D _(Qn) ⊕D _(Q,n−1) , Q ₀ =D _(l,n+1) ⊕D _(ln)I ₁ =D _(Q,n−1) ⊕D _(Q,n−2) , Q ₁ =D _(In) ⊕D _(I,n−1) =I ₂I ₂ =D _(ln) ⊕D _(lI,n−1) , Q ₂ =D _(Qn) ⊕D _(Q,n−1) =I ₀I₃=D_(In), Q₃=D_(Qn)  (1)These values correspond to the four, I channel coded bits which includetwo from the I encoder output and two from the Q encoder output.Analogously, it includes four, Q channel encoded bits.

The values i,j are used as binary coded decimal indices defined asfollows:i=I ₃×2³ +I ₂×2² +I ₁×2¹ +I ₀×2⁰j=Q ₃×2³ +Q ₂×2² +Q ₁×2¹ +Q ₀×2⁰  (2)

The indices i and j may range between zero and 15. A set of basebandsignals are shown in FIG. 3. These symbols may be defined as$\begin{matrix}\begin{matrix}{{s_{1}(t)} = \{ {\begin{matrix}{A,{{{- T_{s}}/2} \leq t \leq 0}} \\{{{1 - {( {1 - A} )\cos^{2}\frac{\pi\quad t}{T_{s}}}},{0 \leq t \leq {T_{s}/2}}}\quad}\end{matrix},{{s_{9}(t)} = {{- s_{1}}(t)}}} } \\{{s_{2}(t)} = \{ {\begin{matrix}{{1 - {( {1 - A} )\cos^{2}\frac{\pi\quad t}{T_{s}}}},{{{- T_{s}}/2} \leq t \leq 0}} \\{A,{0 \leq t \leq {T_{s}/2}}}\end{matrix},{{s_{10}(t)} = {{- s_{2}}(t)}}} } \\{{{s_{3}(t)} = {1 - {( {1 - A} )\cos^{2}\frac{\pi\quad t}{T_{s}}}}},{{{{- T_{s}}/2} \leq t \leq {{T_{s}/2}\quad{s_{11}(t)}}} = {- {s_{3}(t)}}}} \\{{{s_{4}(t)} = {A\quad\sin\quad\frac{\pi\quad t}{T_{s}}}},{{{- T_{s}}/2} \leq t \leq {T_{s}/2}}\quad,{{s_{12}(t)} = {- {s_{4}(t)}}}} \\{{s_{5}(t)} = \{ {\begin{matrix}{{{A\quad\sin\quad\frac{\pi\quad t}{T_{s}}},{{{- T_{s}}/2} \leq t \leq 0}}\quad} \\{{\sin\quad\frac{\pi\quad t}{T_{s}}},{0 \leq t \leq {T_{s}/2}}}\end{matrix},{{s_{13}(t)} = {- {s_{5}(t)}}}} } \\{{s_{6}(t)} = \{ {\begin{matrix}{{\sin\quad\frac{\pi\quad t}{T_{s}}},{{{- T_{s}}/2} \leq t \leq 0}} \\{{A\quad\sin\quad\frac{\pi\quad t}{T_{s}}},{0 \leq t \leq {T_{s}/2}}}\end{matrix},{{s_{14}(t)} = {- {s_{6}(t)}}}} } \\{{{s_{7}(t)} = {\sin\quad\frac{\pi\quad t}{T_{s}}}},{{{- T_{s}}/2} \leq t \leq {T_{s}/2}},{{s_{15}(t)} = {- {s_{7}(t)}}}}\end{matrix} & (3)\end{matrix}$

The pair of indices are used to select which of these baseband signalss_(i)(t), s_(j)(t) will be transmitted respectively over the I and Qchannels in any symbol interval.

For any value of A other than unity, certain waveforms will have adiscontinuous slope at their midpoints (T=0). For example, it has beensuggested that A should equal 1/sqrt(2) to produce minimum envelopefluctuation. When that happens, the waveforms 5 and 6 as well as theirnegatives 13 and 14, will have a discontinuous slope at those midpoints.

Finally, the I and Q baseband signals s_(i)(t)and s_(q)(t)are offset byhalf a symbol relative to one another, and modulated onto the quadraturechannels for transmission.

This trellis-coded characterization of FQPSK is, in principal, an M-arysignaling scheme. This means that a given pair of I and Q data symbolsresults in the transmission of a given pair of I and Q waveforms in eachsignaling interval. Restrictions are placed on the allowable sequencesof waveforms that can be transmitted in either of these channels toproduce continuous I and Q waveform sequences. The present inventorsnoticed that these restrictions on the transitional behavior of thetransmitted signal results in the narrow spectrum characteristic ofFQPSK. The inventors also noticed that the trellis coded structure ofthe transmitter suggests that an optimum receiver for FQPSK should be aform of trellis demodulator. It has been suggested to use of bank of 16biased matched filters followed by a 16 state trellis demodulator. Thisconfiguration is shown in FIG. 4. The simulated bit error rateperformance of this receiver is shown in FIG. 5 and compared with aconventional receiver as well as the performance of conventional uncodedQPSK.

This receiver may be relatively complex, and hence simplifiedconfigurations may be desirable. An averaged matched filter that ismatched to the average of the 16 waveforms may replace the bank of 16matched filters. A reduced complexity of the Viterbi receiver recognizessimilarities in shape properties of certain members of the waveforms,and separates them into different groups. The waveforms s0-s3 aregrouped as a first, composite waveform, with each four waveforms beingsimilarly grouped as follows: $\begin{matrix}\begin{matrix}{{{q_{0}(t)} = {\sum\limits_{i = 0}^{3}{s_{i}(t)}}},} \\{{{q_{1}(t)} = {\sum\limits_{i = 4}^{7}{S_{i}(t)}}},} \\{{q_{2}(t)} = {\sum\limits_{i = 8}^{11}{s_{i}(t)}}} \\{{= {- {q_{0}(t)}}},} \\{{q_{3}(t)} = {\sum\limits_{i = 12}^{15}{s_{i}(t)}}} \\{= {- {q_{1}(t)}}}\end{matrix} & (4)\end{matrix}$

The waveform assignments of the group members are then replaced by theircorresponding average waveform that is, any of s0 to s3 become q0 to q3.This causes the crosscorrelation between the I and Q channels toeffectively disappear. Effectively, the I channel signal is selectedbased on only the I encoder output bits, and the Q channel signal isbased on only the Q encoder output bits. When this happens, then thetrellis coded structure decouples into two independent I and Q two statetrellises; see FIG. 7. The transmitter simplifies into the FIG. 8structure with a corresponding optimum receiver being shown in FIG. 9.The I and Q decisions are no longer produced jointly, but rather areproduced separately by individual Viterbi techniques acting on energybased correlations from the I and Q modulated signals. The degradationin bit error rate relative to the optimum receiver may be compensated bythe significant reduction in complexity of the receiver.

FQPSK, as described above is a convolutional coded modulation. It isrecognized by the inventors that a potentially large coding gain may beachievable using iterative/recursive encoding and decoding ofconcatenated codes with a soft input soft output a posterioriprobability algorithm.

The techniques of concatenated codes are well-known. In general, thissystem has two encoders: an outer coder and an inner coder separated byan interleaver. A serial concatenated code operates serially, while aparallel concatenated code operates in parallel. An outer encoderreceives the uncoded data. The outer coder can be an (n,k) binary linearencoder where n>k. The means that the encoder 200 accepts as input ablock u of k data bits. It produces an output block v of n data bits. Inits simplest form, the outer coder may be a repetition coder. The outercoder codes data with a rate that is less than 1, and may be, forexample, ½ or ⅓.

The interleaver 220 performs a fixed pseudo-random permutation of theblock v, yielding a block w having the same length as v. The permutationcan be an identity matrix, where the output becomes identically the sameas the input. Alternately and more preferably, the permutationrearranges the bits in a specified way.

The inner encoder 210 is a linear rate 1 encoder.

According to a present system, this technique is applied to FQPSK. It isrecognized that the inherent coding that is carried out in FQPSK maysupply the inner code for the iterative concatenated code. In theembodiments, the outer coded signal is applied to a FQPSK system whichmay use the simplified receiver of FIG. 9. The two state Viterbialgorithms are replaced with two state soft input-soft output (SISO)Max-log algorithms as described in the literature. These may beconsidered as modified soft output Viterbi algorithms. Aninterleaving/deinterleaving process is applied between the inner andouter codes. A coding gain from this interleaving process can beobtained by remapping the I and Q FQPSK inner codes from nonrecursiveinto recursive type codes, using other known techniques. FIGS. 10 a-10 bshow the original I and Q encoders and the remapped I and Q encoders forthis purpose.

This remapping provides recursiveness for the parts of the FQPSKencoders that are matched to the reduced two state soft input-softoutput decoder for the inner code.

The remapped encoders would produce different baseband waveforms.However, the allowable FQPSK encoder output sequences would remain thesame. Therefore, both the envelope and spectral characteristics of themodulated signal would be identical to those produced by the FQPSKsignal in the transmitter in FIG. 2.

When an outer code is added, an interleaver is used which has a sizethat is large enough to approximately output an uncorrelated sequence.

FIGS. 11-13 shows three different embodiments of applying an outer codeto the FQPSK modulator/demodulator using a concatenated system withiterative decoding. A number N of input bits 1100 are applied to ademultiplexer 1105 that divides the bits between a pair of outerencoders 1110, 1115 of rate R. These effectively form the I and Qchannel bit streams. Each of the outer-encoded bits are applied tointerleavers 1120, 1121. The I and Q channels are then applied to anFQPSK inner code modulator 1125 which forms the inner code of such asystem. The thus coded stream 1130 is transmitted over the channel 1135.The receiver includes a matched filter bank 1140 with biases, thatproduces I and Q output channels. Each of the channels goes through asoft input-soft output FQPSK demodulator 1145, 1146 whose output iscoupled to a deinterleaver 1150,1151. The resulting I and Q basebandsignals are multiplexed in 1165 to provide the decoded output bits 1170.

In this and the other similar embodiments, the energy biased matchedfilter bank 1140 provides for branch metrics per I and Q channel for thesimplified, two state soft in soft out FQPSK coders. The decoders1145,1146 provide extrinsics associated with the FQPSK encoder inputbits to the outer coder via the deinterleavers 1150, 1151. These areapplied to the outer decoders 1155,1156 to provide new versions of thereceived extrinsics by using the code constraint as an output extrinsicthrough the interleavers. The other outputs are fed back to the inputsof the demodulators 1145,1146.

In operation, the process may repeat/iterate several times. At the endof the final iteration, the output of the outer decoders 1155, 1156 arehard limited in order to produce decisions on the bits.

An alternative system shown in FIG. 12 receives the input bits 1100directly to an outer encoder 1205, and interleaver 1210 whose output isdemultiplexed by 1215 and applied to the FQPSK inner code modulator1220. This system may use an analogous receiver with the matched filterbank 1140, applied to similar demodulators 1145, 1146. The demodulatedoutputs are multiplexed by 1250, and deinterleaved 1255, and then outerdecoded 1260. The feedback loop in this system uses an interleaver 1265and demultiplexer 1270 to provide the I and Q channels.

FIG. 13 shows a parallel concatenated coding system, in which a rate 1outer encoder is formed from the input bitstream and the interleavedinput bitstream as in a turbo code. The input bits 1300 are split withone set of bits being interleaved by 1305. The input bits andinterleaved input bits are applied in parallel to the inner coder/FQPSKmodule which outputs a coded bitstream 1315 that is applied to thechannel 1320. Data from the channel is received into a matched filterbank type receiver 135 that iteratively calculates the output.

The outer coder may simply be a rate ½ repetition outer coder, with ablock interleaver of size n. The outer decoder 1155 may be significantlysimplified for the repetition code. For this code, the outer decoder maysimply swap the order of successive pairs of bits as shown in FIG. 14.

Computer simulations of this system show an improvement of 3.75 dB at upbit error rate of 10⁻⁵.

Although only a few embodiments have been disclosed in detail above,other modifications are possible. All such modifications are intended tobeing comps within the following claims, in which:

1. A method of coding, comprising: passing a sequence of bits to becoded through an outer encoder to produce outer encoded bits; andforming a modified FQPSK modulation on said outer encoded bits of thetype which applies an inner code to said outer coded bits.
 2. A methodas in claim 1, wherein said forming comprises remapping the I and QFQPSK inner codes from nonrecursive into recursive type codes.
 3. Amethod, comprising: outer coding a plurality of bits to form arepetition code; interleaving said bits according to a specifiedinterleaving scheme; and remapped FQPSK modulating the repetition codedbits to form a concatenated code that will be transmitted over achannel.
 4. A method as in claim 3, wherein said remapped concatenatedcode is a parallel concatenated code.
 5. A method as in claim 3, whereinsaid concatenated code is a serial concatenated code.
 6. A method as inclaim 3, further comprising decoding said concatenated code using anFQPSK demodulator in an iterative loop.
 7. A method as in claim 3,wherein said outer coding comprises the multiplexing input bits into inphase and quadrature channels, and separately outer encoding said inphase and quadrature channels.
 8. A method as in claim 3, wherein saidouter encoding comprises outer encoding input bits and thendemultiplexing said input bits into in phase and quadrature channels. 9.A receiver, comprising: a modified FQPSK demodulator, an iterativedecoder, which iteratively demodulates and decodes an input signal. 10.A receiver as in claim 9 further comprising a deinterleaver.
 11. Areceiver as in claim 9, wherein said receiver includes a matched filterbank.
 12. A method, comprising: using a modified FQPSK coding system tocode according to an iterative coding scheme.
 13. A method as in claim12, wherein said iterative coding scheme is a turbo coding type scheme.14. A method as in claim 12, wherein said to using comprises outercoding a signal, and interleaving the signal.
 15. A method as in claim13, wherein said turbo coding scheme is a serial type concatenatedcoding scheme.
 16. A method as in claim 13, wherein said turbo codingscheme is a parallel type concatenated coding scheme.
 17. A method,comprising decoding a modified FQPSK coded signal according to aniterative decoding scheme.
 18. A method as in claim 17, wherein saiddecoding uses a matched filter bank.
 19. A method as in claim 17,wherein said decoding is a turbo decoding scheme using a deinterleaverand an outer decoder.
 20. A method as in claim 17, wherein an FQPSKdemodulation also includes inner decoding.
 21. A method as in claim 17,where the outer code can be of the repetition, convolutional, or blocktype.